Title: The dual Minkowski problem
Speaker: Professor Martin Henk (Technische Universität Berlin)
Time: 2019-10-14 (Monday) 9:00
Inviter: Gangsong Leng, Dongmeng Xi
Abstract: The (classical) Minkowski problem asked for sufficient and necessary conditions such that a finite Borel measure on the sphere is the surface area measure of a convex body. Its solution, based on works by Minkowski, Aleksandrov and Fenchel & Jessen, is one of the centerpieces of the classical Brunn-Minkowski theory. There are two far-reaching extensions of the classical Brunn-Minkowski theory, the Lp-Brunn-Minkowski theory and the dual Brunn-Minkowski theory. In the talk we will discuss the analog of the (classical) Minkowski problem within the dual Brunn-Minkowski theory, i.e., the characterization problem of the dual curvature measures of a convex body. These measures were recently introduced by Huang, Lutwak, Yang and Zhang and they are the counterparts to the area measures within the dual theory.